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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving rational functions of cos > Involving cos(e z)sinh(c z)(a+b cos2(d z))-n





http://functions.wolfram.com/01.19.21.0855.01









  


  










Input Form





Integrate[(Cos[e z] Sinh[c z])/(a + b Cos[d z]^2)^2, z] == (1/4) ((E^((-c + 2 I d - I e) z) ((-2 a - b) (2 a + b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[ 1 - (I (-c - I e))/(2 d), 1, 2 - (I (-c - I e))/(2 d), -((b E^(2 I d z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] - (2 a + b) (-2 a - b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[ 1 - (I (-c - I e))/(2 d), 1, 2 - (I (-c - I e))/(2 d), -((b E^(2 I d z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))] + 2 Sqrt[a] ((2 a^(3/2) + 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[1 - (I (-c - I e))/(2 d), 2, 2 - (I (-c - I e))/(2 d), -((b E^(2 I d z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] + (-2 a^(3/2) - 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[ 1 - (I (-c - I e))/(2 d), 2, 2 - (I (-c - I e))/(2 d), -((b E^(2 I d z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))])))/ (2 a^(3/2) b (a + b)^(3/2) (-c + 2 I d - I e)) - (E^((c + 2 I d - I e) z) ((-2 a - b) (2 a + b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[1 - (I (c - I e))/(2 d), 1, 2 - (I (c - I e))/(2 d), -((b E^(2 I d z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] - (2 a + b) (-2 a - b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[ 1 - (I (c - I e))/(2 d), 1, 2 - (I (c - I e))/(2 d), -((b E^(2 I d z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))] + 2 Sqrt[a] ((2 a^(3/2) + 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[1 - (I (c - I e))/(2 d), 2, 2 - (I (c - I e))/(2 d), -((b E^(2 I d z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] + (-2 a^(3/2) - 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[ 1 - (I (c - I e))/(2 d), 2, 2 - (I (c - I e))/(2 d), -((b E^(2 I d z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))])))/ (2 a^(3/2) b (a + b)^(3/2) (c + 2 I d - I e)) + (E^((-c + 2 I d + I e) z) ((-2 a - b) (2 a + b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[1 - (I (-c + I e))/(2 d), 1, 2 - (I (-c + I e))/(2 d), -((b E^(2 I d z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] - (2 a + b) (-2 a - b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[1 - (I (-c + I e))/(2 d), 1, 2 - (I (-c + I e))/(2 d), -((b E^(2 I d z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))] + 2 Sqrt[a] ((2 a^(3/2) + 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[1 - (I (-c + I e))/(2 d), 2, 2 - (I (-c + I e))/(2 d), -((b E^(2 I d z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] + (-2 a^(3/2) - 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[ 1 - (I (-c + I e))/(2 d), 2, 2 - (I (-c + I e))/(2 d), -((b E^(2 I d z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))])))/ (2 a^(3/2) b (a + b)^(3/2) (-c + 2 I d + I e)) - (E^((c + 2 I d + I e) z) ((-2 a - b) (2 a + b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[1 - (I (c + I e))/(2 d), 1, 2 - (I (c + I e))/(2 d), -((b E^(2 I d z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] - (2 a + b) (-2 a - b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[ 1 - (I (c + I e))/(2 d), 1, 2 - (I (c + I e))/(2 d), -((b E^(2 I d z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))] + 2 Sqrt[a] ((2 a^(3/2) + 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[1 - (I (c + I e))/(2 d), 2, 2 - (I (c + I e))/(2 d), -((b E^(2 I d z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] + (-2 a^(3/2) - 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[ 1 - (I (c + I e))/(2 d), 2, 2 - (I (c + I e))/(2 d), -((b E^(2 I d z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))])))/ (2 a^(3/2) b (a + b)^(3/2) (c + 2 I d + I e)))










Standard Form





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- </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> e </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> d </mi> </mrow> </mfrac> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> e </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> d </mi> </mrow> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;2&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;1&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, FractionBox[RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;c&quot;, &quot;-&quot;, RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, &quot;e&quot;]]]], &quot;)&quot;]]]], RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;d&quot;]]]]], Hypergeometric2F1], &quot;,&quot;, TagBox[&quot;2&quot;, Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], &quot;;&quot;, 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<times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <ci> b </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> d </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <ci> b </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <ci> b </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> d </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <ci> b </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18